Finite Group Databasebeta

← #33104531

Subgroups — #33104531

Order 18688.

944 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988659C211yesmaximal, characteristic
2C2×D4×#10596831C211yesmaximal, characteristic
3#22610655C211yesmaximal, characteristic, complemented
4#22610650C211yesmaximal, characteristic, complemented
5#22610116C211yesmaximal, characteristic, complemented
6#22610111C211yesmaximal, characteristic, complemented
7#22610111C211yesmaximal, characteristic, complemented
8#22610111C211yesmaximal, characteristic, complemented
9#22610051C211yesmaximal, characteristic, complemented
10#22609915C211yesmaximal, characteristic, complemented
11#22609911C211yesmaximal, characteristic, complemented
12#22609788C211yesmaximal, characteristic, complemented
13#22609628C211yesmaximal, characteristic, complemented
14C2×#17988342C211yesmaximal, characteristic, complemented
15C73×#2290C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18C23×#10596831C2211yescharacteristic
19C23×#10596831C2211yescharacteristic
20#17988659—24no—
21D4×#10596831—24no—
22C2×C4⋊#10596831C2211yescharacteristic
23C2×C4⋊#10596831C2211yescharacteristic
24C2×C4⋊#10596831C2211yescharacteristic
25C2×C4⋊#10596831C2211yescharacteristic
26C2×C4⋊#10596831C2211yescharacteristic
27C2×C4⋊#10596831C2211yescharacteristic
28C2×C4⋊#10596831C2211yescharacteristic
29C2×C4⋊#10596831C2211yescharacteristic
30C2×C22⋊#10596831C2211yescharacteristic
31C2×C22⋊#10596831C2211yescharacteristic
32C2×C22⋊#10596831C2211yescharacteristic
33C2×C22⋊#10596831C2211yescharacteristic
34C2×#14556502C2211yescharacteristic
35C2×C4×#10596831C2211yescharacteristic
36#17988342C2211yescharacteristic
37#17988342C2211yescharacteristic
38#17988342C2211yescharacteristic
39#17988342C2211yescharacteristic
40#17988342C2211yescharacteristic
41#17988342C2211yescharacteristic
42#17988342C2211yescharacteristic
43#17988342C2211yescharacteristic
44#17988342C2211yescharacteristic
45#17988342C2211yescharacteristic
46C2×C4×D4×C73C2211yescharacteristic
47C2×#117×C73C2211yescharacteristic
48C22×C42×C73C2211yescharacteristic
49#388×C73C411yescharacteristic
50#388×C73C411yescharacteristic
51#387×C73C411yescharacteristic
52#387×C73C411yescharacteristic
53#386×C73C411yescharacteristic
54#386×C73C411yescharacteristic
55#385×C73C411yescharacteristic
56#385×C73C411yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58C4×C22⋊C4×C73C2211yescharacteristic
59C4×C22⋊C4×C73C2211yescharacteristic
60#376×C73C2211yescharacteristic
61C2×#11924012—22no—
62C2×#11924012—22no—
63C2×#11924012—41no—
64C22×#10596831—22no—
65C22×#10596831—22no—
66C22×#10596831—22no—
67C22×#10596831—22no—
68C22×#10596831—22no—
69C22×#10596831—22no—
70C22×#10596831—41no—
71C22×#10596831—41no—
72C22×#10596831—41no—
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76C22×#10596831C2311yescharacteristic
77C22×#10596831C2311yescharacteristic
78C22×#10596831C2311yescharacteristic
79C22×#10596831C2311yescharacteristic
80C22×#10596831C2311yescharacteristic
81C4⋊#10596831—22no—
82C4⋊#10596831—22no—
83C4⋊#10596831—22no—
84C4⋊#10596831—22no—
85C4⋊#10596831—41no—
86C4⋊#10596831—41no—
87C4⋊#10596831—41no—
88C4⋊#10596831—41no—
89C22⋊#10596831—22no—
90C22⋊#10596831—22no—
91C22⋊#10596831—22no—
92C22⋊#10596831—22no—
93#14556502—22no—
94C4×#10596831—22no—
95C22×D4×C73C2×C411yescharacteristic
96C23×C4×C73C2×C411yescharacteristic
97C23×C4×C73C2×C411yescharacteristic
98C23×C4×C73C2311yescharacteristic
99C23×C4×C73C2311yescharacteristic
100C4×D4×C73D414yes—
101C4×D4×C73Q814yes—
102#117×C73—41no—
103#117×C73—41no—
104C2×C4⋊C4×C73C2×C411yescharacteristic
105C2×C4⋊C4×C73C2×C411yescharacteristic
106C2×C4⋊C4×C73C2×C411yescharacteristic
107C2×C4⋊C4×C73C2×C411yescharacteristic
108C2×C4⋊C4×C73C2×C411yescharacteristic
109C2×C22⋊C4×C73C2×C411yescharacteristic
110C2×C22⋊C4×C73C2×C411yescharacteristic
111C2×C22⋊C4×C73C2×C411yescharacteristic
112C2×C22⋊C4×C73C2×C411yescharacteristic
113C2×C22⋊C4×C73C2×C411yescharacteristic
114C2×C22⋊C4×C73C2×C411yescharacteristic
115C2×C22⋊C4×C73C2×C411yescharacteristic
116C2×C22⋊C4×C73C2×C411yescharacteristic
117C2×C42×C73—41no—
118C2×C42×C73—41no—
119C2×C42×C73C2×C411yescharacteristic
120C2×C42×C73C2×C411yescharacteristic
121C2×C42×C73C2311yescharacteristic
122C2×C42×C73C2311yescharacteristic
123C2×C42×C73C2311yescharacteristic
124C2×C42×C73C2311yescharacteristic
125C2×C42×C73C2311yescharacteristic
126#95×C73C2×C411yescharacteristic
127#95×C73C2×C411yescharacteristic
128#95×C73C2×C411yescharacteristic
129#95×C73C2×C411yescharacteristic
130#95×C73C2×C411yescharacteristic
131#95×C73C2×C411yescharacteristic
132#95×C73C2×C411yescharacteristic
133#95×C73C2×C411yescharacteristic
134#95×C73C2×C411yescharacteristic
135#95×C73C2×C411yescharacteristic
136#11924012—44no—
137C2×#10596831—21no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—21no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831—21no—
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—44no—
160C2×#10596831—44no—
161C2×#10596831—44no—
162C2×#10596831#4112yes—
163C2×#10596831#4112yes—
164C24×C73C22×C411yescharacteristic
165C24×C73C22×C411yescharacteristic
166C2×D4×C73—22no—
167C2×D4×C73—22no—
168C2×D4×C73C4⋊C414yes—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—22no—
178C22×C4×C73—22no—
179C22×C4×C73—22no—
180C22×C4×C73—41no—
181C22×C4×C73—41no—
182C22×C4×C73—41no—
183C22×C4×C73C22×C411yescharacteristic
184C22×C4×C73C22×C411yescharacteristic
185C22×C4×C73C22×C411yescharacteristic
186C22×C4×C73C22×C411yescharacteristic
187C22×C4×C73C22×C411yescharacteristic
188C22×C4×C73C22×C411yescharacteristic
189C22×C4×C73C22×C411yescharacteristic
190C22×C4×C73C22×C411yescharacteristic
191C22×C4×C73C22×C411yescharacteristic
192C22×C4×C73C22×C411yescharacteristic
193C22×C4×C73C22×C411yescharacteristic
194C22×C4×C73C22×C411yescharacteristic
195C22×C4×C73C2×D412yes—
196C22×C4×C73C2×D412yes—
197C22×C4×C73C2×Q812yes—
198C22×C4×C73C2×Q812yes—
199C22×C4×C73C2411yescharacteristic
200C4⋊C4×C73—22no—
201C4⋊C4×C73—41no—
202C4⋊C4×C73—41no—
203C4⋊C4×C73—41no—
204C4⋊C4×C73C4⋊C414yes—
205C22⋊C4×C73—22no—
206C22⋊C4×C73—22no—
207C22⋊C4×C73—22no—
208C22⋊C4×C73—41no—
209C22⋊C4×C73—41no—
210C22⋊C4×C73—41no—
211C22⋊C4×C73C4⋊C414yes—
212C22⋊C4×C73C4⋊C414yes—
213C42×C73—21no—
214C42×C73—21no—
215C42×C73—21no—
216C42×C73—21no—
217C42×C73—21no—
218C42×C73—21no—
219C42×C73—21no—
220C42×C73—21no—
221C42×C73—41no—
222C42×C73—41no—
223C42×C73C2×D412yes—
224C42×C73C2×Q812yes—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73C2×C4⋊C412yes—
236C23×C73C2×C4⋊C412yes—
237C23×C73#13112yes—
238C23×C73#13112yes—
239C23×C73C23×C411yescharacteristic
240D4×C73—28no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—22no—
252C2×C4×C73—22no—
253C2×C4×C73—22no—
254C2×C4×C73—22no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—44no—
281C2×C4×C73—44no—
282C2×C4×C73C2×C4⋊C412yes—
283C2×C4×C73C2×C4⋊C412yes—
284C2×C4×C73C2×C4⋊C412yes—
285C2×C4×C73C2×C4⋊C412yes—
286C2×C4×C73#13112yes—
287C2×C4×C73C22×D411yescharacteristic
288C2×C4×C73C22×Q811yescharacteristic
289C2×C4×C73C2×#4111yescharacteristic
290C2×C4×C73C2×#4111yescharacteristic
291C2×C4×C73H(5,𝔽2)11yescharacteristic
292C2×C4×C73H(5,𝔽2)11yescharacteristic
293#10596831—22no—
294#10596831—22no—
295#10596831—41no—
296#10596831—41no—
297#10596831—41no—
298#10596831—41no—
299#10596831—41no—
300#10596831—41no—
301C22×C73—22no—
302C22×C73—22no—
303C22×C73—22no—
304C22×C73—22no—
305C22×C73—22no—
306C22×C73—22no—
307C22×C73—22no—
308C22×C73—22no—
309C22×C73—22no—
310C22×C73—41no—
311C22×C73—41no—
312C22×C73—41no—
313C22×C73—41no—
314C22×C73#42414yes—
315C22×C73C22×C4⋊C411yescharacteristic
316C22×C73C4×#4111yescharacteristic
317C22×C73#51811yescharacteristic
318C22×C73C2×#13111yescharacteristic
319C22×C73C2×#13111yescharacteristic
320C22×C73C2×#13111yescharacteristic
321C22×C73#56811yescharacteristic
322C4×C73—22no—
323C4×C73—22no—
324C4×C73—22no—
325C4×C73—22no—
326C4×C73—22no—
327C4×C73—41no—
328C4×C73—41no—
329C4×C73—41no—
330C4×C73—41no—
331C4×C73—41no—
332C4×C73—41no—
333C4×C73—41no—
334C4×C73#54611yescharacteristic
335C4×C73#54611yescharacteristic
336C4×C73#55411yescharacteristic
337C4×C73#55411yescharacteristic
338#22697—731nomaximal, Sylow
339C2×C73—24no—
340C2×C73—42no—
341C2×C73#234911yescharacteristic
342C2×C73C2×#42411yescharacteristic
343C2×C73#290611yescharacteristic
344C2×C73#296611yescharacteristic
345C2×C73#296811yescharacteristic
346C2×C73#297611yescharacteristic
347C2×C73#297711yescharacteristic
348C2×#435—731no—
349C2×C8×D4—731no—
350#2290D7311yescharacteristic
351#1940—731no—
352#1939—731no—
353#1851—731no—
354#1850—731no—
355#1850—731no—
356#1850—731no—
357#1832—731no—
358#1798—731no—
359#1797—731no—
360#1768—731no—
361#1729—731no—
362C2×#336—731no—
363C73#2269711yescharacteristic, complemented, Sylow
364C22×M16—731no—
365C23×C8—731no—
366C23×C8—731no—
367C23×C8—731no—
368C2×C4×D4C2×D7311yescharacteristic
369C2×#117C2×D7311yescharacteristic
370C22×C42C2×D7311yescharacteristic
371#435—1464no—
372C8×D4—1464no—
373C2×C4⋊C8—731no—
374C2×C4⋊C8—731no—
375C2×C4⋊C8—731no—
376C2×C4⋊C8—731no—
377C2×C4⋊C8—731no—
378C2×C4⋊C8—731no—
379C2×C4⋊C8—731no—
380C2×C4⋊C8—731no—
381C2×C22⋊C8—731no—
382C2×C22⋊C8—731no—
383C2×C22⋊C8—731no—
384C2×C22⋊C8—731no—
385C2×#97—731no—
386C2×C4×C8—731no—
387#388Dic7311yescharacteristic
388#388Dic7311yescharacteristic
389#387Dic7311yescharacteristic
390#387Dic7311yescharacteristic
391#386Dic7311yescharacteristic
392#386Dic7311yescharacteristic
393#385Dic7311yescharacteristic
394#385Dic7311yescharacteristic
395C4×C4⋊C4C2×D7311yescharacteristic
396C4×C22⋊C4C2×D7311yescharacteristic
397C4×C22⋊C4C2×D7311yescharacteristic
398#376C2×D7311yescharacteristic
399#336—731no—
400#336—731no—
401#336—731no—
402#336—731no—
403#336—731no—
404#336—731no—
405#336—731no—
406#336—731no—
407#336—731no—
408#336—731no—
409C22×D4C2×Dic7311yescharacteristic
410C23×C4C2×Dic7311yescharacteristic
411C23×C4C2×Dic7311yescharacteristic
412C23×C4C22×D7311yescharacteristic
413C23×C4C22×D7311yescharacteristic
414C2×M16—2921no—
415C2×M16—1462no—
416C2×M16—1462no—
417C22×C8—2921no—
418C22×C8—2921no—
419C22×C8—2921no—
420C22×C8—731no—
421C22×C8—731no—
422C22×C8—731no—
423C22×C8—731no—
424C22×C8—731no—
425C22×C8—731no—
426C22×C8—731no—
427C22×C8—731no—
428C22×C8—1462no—
429C22×C8—1462no—
430C22×C8—1462no—
431C22×C8—1462no—
432C22×C8—1462no—
433C22×C8—1462no—
434C4×D4Dic14614yes—
435C4×D4D29214yes—
436#117—41no—
437#117—41no—
438C2×C4⋊C4C2×Dic7311yescharacteristic
439C2×C4⋊C4C2×Dic7311yescharacteristic
440C2×C4⋊C4C2×Dic7311yescharacteristic
441C2×C4⋊C4C2×Dic7311yescharacteristic
442C2×C4⋊C4C2×Dic7311yescharacteristic
443C2×C22⋊C4C2×Dic7311yescharacteristic
444C2×C22⋊C4C2×Dic7311yescharacteristic
445C2×C22⋊C4C2×Dic7311yescharacteristic
446C2×C22⋊C4C2×Dic7311yescharacteristic
447C2×C22⋊C4C2×Dic7311yescharacteristic
448C2×C22⋊C4C2×Dic7311yescharacteristic
449C2×C22⋊C4C2×Dic7311yescharacteristic
450C2×C22⋊C4C2×Dic7311yescharacteristic
451C2×C42—41no—
452C2×C42—41no—
453C2×C42C2×Dic7311yescharacteristic
454C2×C42C2×Dic7311yescharacteristic
455C2×C42C22×D7311yescharacteristic
456C2×C42C22×D7311yescharacteristic
457C2×C42C22×D7311yescharacteristic
458C2×C42C22×D7311yescharacteristic
459C2×C42C22×D7311yescharacteristic
460C4⋊C8—2921no—
461C4⋊C8—2921no—
462C4⋊C8—2921no—
463C4⋊C8—2921no—
464C4⋊C8—1462no—
465C4⋊C8—1462no—
466C4⋊C8—1462no—
467C4⋊C8—1462no—
468C22⋊C8—1462no—
469C22⋊C8—1462no—
470C22⋊C8—1462no—
471C22⋊C8—1462no—
472#97—1462no—
473C4×C8—1462no—
474#95C2×Dic7311yescharacteristic
475#95C2×Dic7311yescharacteristic
476#95C2×Dic7311yescharacteristic
477#95C2×Dic7311yescharacteristic
478#95C2×Dic7311yescharacteristic
479#95C2×Dic7311yescharacteristic
480#95C2×Dic7311yescharacteristic
481#95C2×Dic7311yescharacteristic
482#95C2×Dic7311yescharacteristic
483#95C2×Dic7311yescharacteristic
484C24C22×Dic7311yescharacteristic
485C24C22×Dic7311yescharacteristic
486C2×D4—22no—
487C2×D4—22no—
488C2×D4C4⋊Dic7314yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4C22×Dic7311yescharacteristic
504C22×C4C22×Dic7311yescharacteristic
505C22×C4C22×Dic7311yescharacteristic
506C22×C4C22×Dic7311yescharacteristic
507C22×C4C22×Dic7311yescharacteristic
508C22×C4C22×Dic7311yescharacteristic
509C22×C4C22×Dic7311yescharacteristic
510C22×C4C22×Dic7311yescharacteristic
511C22×C4C22×Dic7311yescharacteristic
512C22×C4C22×Dic7311yescharacteristic
513C22×C4C22×Dic7311yescharacteristic
514C22×C4C22×Dic7311yescharacteristic
515C22×C4C2×D29212yes—
516C22×C4C2×D29212yes—
517C22×C4C2×Dic14612yes—
518C22×C4C2×Dic14612yes—
519C22×C4C23×D7311yescharacteristic
520M16—2924no—
521C2×C8—2924no—
522C2×C8—2924no—
523C2×C8—2924no—
524C2×C8—732no—
525C2×C8—732no—
526C2×C8—1461no—
527C2×C8—1461no—
528C2×C8—1461no—
529C2×C8—1461no—
530C2×C8—1461no—
531C2×C8—1461no—
532C2×C8—1461no—
533C2×C8—1461no—
534C2×C8—1461no—
535C2×C8—1461no—
536C2×C8—1461no—
537C2×C8—1461no—
538C2×C8—1461no—
539C2×C8—1461no—
540C2×C8—1461no—
541C2×C8—1461no—
542C2×C8—1461no—
543C2×C8—1461no—
544C2×C8—1461no—
545C2×C8—1461no—
546C2×C8—1461no—
547C2×C8—1461no—
548C4⋊C4—22no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4C4⋊Dic7314yes—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4C4⋊Dic7314yes—
560C22⋊C4C4⋊Dic7314yes—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—41no—
570C42—41no—
571C42C2×D29212yes—
572C42C2×Dic14612yes—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23C2×C4⋊Dic7312yes—
584C23C2×C4⋊Dic7312yes—
585C23#1455659812yes—
586C23#1455659812yes—
587C23C23×Dic7311yescharacteristic
588D4—28no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—44no—
629C2×C4—44no—
630C2×C4C2×C4⋊Dic7312yes—
631C2×C4C2×C4⋊Dic7312yes—
632C2×C4C2×C4⋊Dic7312yes—
633C2×C4C2×C4⋊Dic7312yes—
634C2×C4#1455659812yes—
635C2×C4C22×D29211yescharacteristic
636C2×C4C22×Dic14611yescharacteristic
637C2×C4#41×D7311yescharacteristic
638C2×C4#41×D7311yescharacteristic
639C2×C4#1455663611yescharacteristic
640C2×C4#1455663611yescharacteristic
641C8—2921no—
642C8—2921no—
643C8—2921no—
644C8—2921no—
645C8—2921no—
646C8—2921no—
647C8—1462no—
648C8—1462no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22#1798861414yes—
663C22C22×C4⋊Dic7311yescharacteristic
664C22#41×Dic7311yescharacteristic
665C22#1798906211yescharacteristic
666C22C2×#1455659811yescharacteristic
667C22C2×#1455659811yescharacteristic
668C22C2×#1455659811yescharacteristic
669C22#1798935411yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—22no—
674C4—22no—
675C4—41no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—41no—
682C4#1798923211yescharacteristic
683C4#1798923211yescharacteristic
684C4#1798929611yescharacteristic
685C4#1798929611yescharacteristic
686C2—24no—
687C2—42no—
688C2#2261284111yescharacteristic
689C2C2×#1798861411yescharacteristic
690C2#2261849911yescharacteristic
691C2#2261890711yescharacteristic
692C2#2261892711yescharacteristic
693C2#2261897911yescharacteristic
694C2#2261898711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#2290C2
prime radicalC22×D4×C73C2×C4
cosocleC22×C4×C73C24
hypercenter#2290D73
hypocenterC73#22697
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #2290

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #22610655C2semidirect
4. #22610650C2semidirect
5. #22610116C2semidirect
6. #22610111C2semidirect
7. #22610111C2semidirect
8. #22610111C2semidirect
9. #22610051C2semidirect
10. #22609915C2semidirect
11. #22609911C2semidirect
12. #22609788C2semidirect
13. #22609628C2semidirect
14. C2×#17988342C2semidirect
363. C73#22697semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179886592
C2×D4×#105968312
#226106552
#226106502
#226101162
#226101112
#226100512
#226099152
#226099112
#226097882
#226096282
C2×#179883422
C73×#22902
#2269773